Sigma-delta modulation has recently been a popular technique for obtaining high resolution data conversion. In such technique, high resolution results from oversampling, noise-shaping as well as noise filtering. Such technique has been successfully applied to DC measurement, voice band, audio processing, ISDN and communication system, etc. For detail discussion of sigma-delta modulation techniques, relevant to the principles and terminology that follows in the context, please refer to a selected reprint volume entitled "Overampling delta-sigma data converters", edited by J. C. Candy and G. C. Temes, IEEE Press, 1992.
One-bit sigma-delta modulators have achieved popularity for use in integrated circuit data converters due to the fact they employ a 1-bit internal DAC that dose not require precision component matching. However, the resolution that a 1-bit sigma-delta modulator can achieve at a given oversampling ratio is limited. Although the achievable resolution dose improve with increasing loop filter order, these improvements diminish rapidly due to instability. In addition, because of the substantial out-of-band quantization noise power in sigma-delta modulators, the design of analog output filters for oversampled digital-to-analog (D/A) converters can be quite difficult. One solution to the above problems is to use multibit quantization in the sigma-delta converters.
The primary advantage of sigma-delta modulators employing multibit quantization is that the quantization noise power can be reduced typically by 6 dB per additional bit. Therefore, we can increase the converter resolution without increasing the oversampling ratio. An additional benefit of multibit quantization is that it enhances the modulator stability. However, the internal multibit feedback digital-to-analog converter (DAC) of the multibit sigma-delta converter must have the same stringent linearity as the overall converter. This is because any internal DAC output conversion errors directly appear in the sigma-delta converter output, and moreover they can not be shaped by the modulator's loop filter.
The internal multibit DACs are commonly implemented with a plurality of unit components, such as capacitors, resistors, or current switches. For example, an internal multibit DAC can utilize a capacitor array wherein a digital input code is encoded into a set of control signals to select charging capacitors. The total stored charge is redistributed to provide an analog output voltage in response to the digital input code. Conventionally, to implement an N-level capacitive internal DAC requires (N-1) capacitors, where N is an integer greater than two. Component variations make the internal DAC transfer curve nonlinear. The linearity error manifests itself in the frequency domain in the form of distortion components at harmonic frequencies of the signal frequency.
To solve the nonlinearity problem in an internal DAC having a plurality of components, the prior art approach of digital self-calibration technique has been used to correct the internal DAC nonlinearity, as described in M. Sarhang-Nejad and G. C. Temes, "A high resolution multibit sigma-delta ADC with digital correction and relaxed amplifier requirements," IEEE Journal of Solid-State Circuits, pp. 648-990 (June, 1993). The technique typically require additional calibration circuits and increase circuit area and complexity.
Another known internal DAC nonlinearity correction approaches in oversampling converters are utilizing dynamic element matching techniques. The randomization of component switching breaks the nonlinearity error from noticeable discrete-frequency distortions in the baseband into random white noise which is spread over half of the sampling frequency, as described in R. Careley, "A noise-shaping coder topology for 15+bit converter," IEEE Journal of Solid-State Circuits, pp. 267-273 (April, 1989). In order to accomplish the random switching in an internal DAC having a plurality of components, such as a capacitor array, switching control signals are generated by a random number generator. Because only a pseudo-random number generator is physically possible implemented, not all of the nonlinearity error is converted from discrete-frequency distortions into random white noise.
A popular dynamic element matching technique called data weighted averaging (DWA) method can shape the distortions introduced by the non-ideal internal DAC to high frequencies where they can be removed by the following filtering, as described in R. T. Baird and T. S. Fiez, "Linearity enhancement of multibit sigma-delta A/D and D/A converters using data weighted averaging," IEEE Transactions on Circuits and Systems II, pp. 753-762 (December 1995). However, when the DWA method is applied to an internal multibit DAC of the multibit sigma-delta converter, substantial baseband tones and intermodulation distortions resulting from aliasing of the internal multibit DAC noise are found and they limit the performance of the overall sigma-delta converter. This problem plays a significant obstacle for utilizing the DWA method in a multibit sigma-delta converter. For tackling this problem, one can add dither in a multibit sigma-delta converter to break up and randomize the aliasing baseband tones, at cost of increasing baseband noise, reducing dynamic range, and possibly destabilizing the converter. Therefore, an efficient method for reducing baseband tones without adding dither in a multibit sigma-delta converter employing data weighted averaging method is necessary.